Author : Alan M. Cohen
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 48,13 MB
Release : 2007-06-16
Category : Mathematics
ISBN : 0387688552
This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.
Author : Richard Bellman
Publisher : World Scientific
Page : 180 pages
File Size : 16,57 MB
Release : 1984
Category : Mathematics
ISBN : 9789971966737
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.
Author : Urs Graf
Publisher : Birkhäuser
Page : 501 pages
File Size : 34,20 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 303487846X
The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications.
Author : Dean G. Duffy
Publisher : CRC Press
Page : 727 pages
File Size : 23,91 MB
Release : 2004-07-15
Category : Mathematics
ISBN : 1420035142
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana
Author : Joel L. Schiff
Publisher :
Page : 252 pages
File Size : 29,61 MB
Release : 2014-01-15
Category :
ISBN : 9781475772616
Author : Claude Brezinski
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 15,19 MB
Release : 2002-06-30
Category : Mathematics
ISBN : 9781402007118
The main objective of this volume is to create a bridge between control theory and its numerical analysis aspects. It is unique because it presents both subjects in a single volume. The book combines an exposition of linear control theory and the corresponding modern relevant computational techniques such as orthogonal polynomials, Padé approximation, numerical linear algebra, and some topics on nonlinear differential equations. It can be considered as an introduction to control theory for numerical analysts looking for a wide area of applications and as an introduction to recent numerical methods for control specialists. Audience: Aimed at advanced students at a doctoral or post-doctoral level, engineers, and researchers in control theory and numerical analysis.
Author : You-He Zhou
Publisher : Springer Nature
Page : 478 pages
File Size : 12,86 MB
Release : 2021-03-09
Category : Technology & Engineering
ISBN : 9813366435
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
Author : John F. Monahan
Publisher : Cambridge University Press
Page : 465 pages
File Size : 41,83 MB
Release : 2011-04-18
Category : Computers
ISBN : 1139498002
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Author : Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher : CRC Press
Page : 556 pages
File Size : 15,90 MB
Release : 1961
Category : Science
ISBN : 9780677200507
Author : Winfried K. Grassmann
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 16,81 MB
Release : 2000
Category : Business & Economics
ISBN : 9780792386179
Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership. The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail: Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.
